Question

Voltage sags and swells. The power quality of a transformer is measured by the quality of the voltage. Two causes of poor power quality are “sags” and “swells.” A sag is an unusual dip and a swell is an unusual increase in the voltage level of a transformer. The power quality of transformers built in Turkey was investigated in Electrical Engineering (Vol. 95, 2013). For a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. Assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week.

a. For a sag distribution with any shape, analyze what proportion of transformers will have between 263 and 443 sags per week. As part of your answer, explain the rule you applied and justify your answer. (5 marks)

b. For a sag distribution that is mound-shaped and symmetric, analyze what proportion of transformers will have between 263 and 443 sags per week. As part of your answer, explain the rule you applied and justify your answer. (5 marks)

c. For a swell distribution with any shape, analyze what proportion of transformers will have between 109 and 259 swells per week. As part of your answer, explain the rule you applied and justify your answer. (5 marks)

d. For a swell distribution that is mound-shaped and symmetric, analyze what proportion of transformers will have between 109 and 259 swells per week. As part of your answer, explain the rule you applied and justify your answer. (5 marks)

Answer 1

Answer:

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Answer 2

Answer:

a

z-scores = 1.57

b

z-score s = 3.36